Topics: Graph Theory
(lemma)
If a graph with no loops has edges and vertices, then the sum of its vertices’ degrees is twice the number of edges.
That is:
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- Attribute
- Attribute Value
- Binary Tree
- Candidate Key
- Class B IP Address
- Class B Subnetting
- Database
- Database Normalisation
- Doubly Linked List
- First Normal Form
- Foreign Key
- Functional Dependency
- List
- Non-Prime Attribute
- Partial Dependency
- Primary Key
- Queue
- Relation (database)
- Search Binary Tree
- Second Normal Form
- Simple Linked List
- Software Engineering
- Stack
- Subnetting
- Superkey
- Third Normal Form
- Transitive Dependency
- Tree (Data Structure)
- Tuple
- « Plus » Pronunciation
- Alternation
- Alveolo-Palatal Consonant
- Anaphora
- Anaphora (Rhetoric)
- Antecedent
- Arbitrariness of Language
- Auslan
- Cataphora
- Coronal Consonant
- Deixis
- Displacement of Language
- Duality of Patterning
- Endophora
- German -ung Words
- German Definite Article Declension
- German Language
- Hocket's Design Features
- Iconic Sign
- Ideophone
- Indexical Sign
- Jespersen's Cycle
- Language
- Lexical Set
- Lexical Sets in English
- Linguistics
- Metathesis
- Nonrestrictive Clause
- Onomatopoeia
- Palato-Alveolar Consonant
- Prevarication
- Pro-form
- Productivity of Language
- Reflexiveness of Language
- Relative Clause
- Restrictive Clause
- Retroflex Consonant
- Semiotics
- Sign
- Spoken Language Comes Before Written Language
- Symbolic Sign
- Traditional Transmission
- 2024-03-20, Probabilidades de Absorción (PE)
- Absolute Error
- Absolute Minimal and Maximal Elements
- Absolutely Continuous Random Variable
- Absolutely Convergent Series
- Absorbing Markov Chain
- Absorbing Set
- Accumulation Point
- Addition Principle
- Algebra
- Angle Between Lines
- Angle Between Planes
- Angle Between Vectors
- Antiderivative of a Vector-Valued Function
- Approximation Order of a Function
- Arc
- Arc Length
- Arc Length Parameter
- Arithmetic Mean
- Arithmetic Mean for a Set of Frequencies
- Arithmetic Mean for Grouped Data
- Articulation Point
- Associated Matrix of a Linear Transformation
- Associated Matrix of Composed Transformations
- Associated Matrix of Operated Transformations
- Asymmetric Digraph
- Asymptotically Unbiased Estimator
- Average First-Passage Time
- Balanced Digraph
- Bar Chart
- Bayes' Theorem
- Bernoulli Distribution
- Bernoulli Process
- Bernoulli Trial
- Bias (Statistics)
- Bijective Linear Transformations
- Binomial Distribution
- Binormal Vector
- Bipartite Graph
- Bisection Method
- Block
- Boolean Matrix
- Boundary Point
- Box Plot
- Branch Vertex
- Bridge
- Bubble Graph
- Càdlàg Function
- Calculation of Eigenvalues and Eigenvectors
- Calculus
- Cartesian Product
- Cayley-Hamilton Theorem
- Central Limit Theorem
- Centre of a Tree
- Chain
- Change of Basis Matrix
- Chapman-Kolmogorov Equation
- Characteristic Function
- Characteristic Polynomial
- Characteristic Polynomial of a Diagonalisable Transformation
- Chi-Squared Distribution
- Circuit
- Closed Neighbourhood
- Closed Set
- Closure
- Combination
- Compact Set
- Comparability
- Complement of a Graph
- Complete Bipartite Graph
- Complete Digraph
- Complete Graph
- Composition of Relations
- Conditional Density Function
- Conditional Probability
- Conjugate Transpose Matrix
- Connected Digraph
- Connected Graph
- Conservative Vector Field
- Consistent Estimator
- Continuous Function
- Continuous Process
- Continuous Uniform Distribution
- Continuous Vector-Valued Function
- Continuous Vectorial Function
- Contour Line
- Convergence Order of a Numerical Method
- Convergence Speed of a Sequence
- Convergence Tests for Series
- Coordinate Vector
- Covariance
- Cramér-Rao Lower Bound
- Curl of a Vector Field
- Curvature
- Curve
- Cyclical Markov Chain
- Data (Statistics)
- Defined Integral of a Vector-Valued Function
- Density and Distribution Function of a Dependent Random Variable
- Density Function
- Density Function of a Random Vector
- Derivative of a Vector-Valued Function
- Derivative of Operated Vector-Valued Functions
- Descriptive Mathematical Model
- Descriptive Statistics
- Deterministic Mathematical Model
- Diagonal Associated Matrix
- Diagonalisation of a Linear Transformation
- Diagonalisation Test
- Digraph
- Discounted Policy Improvement Method for MDPs
- Discrete Random Variable
- Discrete Uniform Distribution
- Dispersion Graph
- Distance Between a Line and a Point
- Distance Between Two Lines
- Distance from a Plane to a Point
- Distribution Function
- Distribution Function From the Left
- Divergence of a Vector Field
- Domain and Range of a Relation
- Eccentricity
- Edge
- Edge-Disjoint Subgraphs
- Efficient Estimator
- Eigenspace
- Eigenvalues and Eigenvectors
- Empty Set
- Equal Functions
- Equivalence Class
- Equivalence Relation
- Ergodic Markov Chain
- Ergodic Set
- Error Propagation
- Estimator
- Eulerian Path
- Event
- Event Independence
- Excess Kurtosis
- Exhaustive Enumeration Method for MDPs
- Expanded Subgraph
- Expected Amount of Bets Before Ruin in the Gambler's Ruin Problem
- Expected Long Term Cost for a Policy in an MDP
- Expected Total Cost of an MDP Starting from a State
- Expected Value
- Expected Value and Variance of the Mean of a Random Sample
- Expressing a Piecewise Function with Shifted Unit Step Functions
- F Distribution
- False Position Method
- Finite and Stationary Markov Chain
- First-Passage Time
- Floating Point Form of Real Numbers
- Forest
- Frequency
- Function
- Fundamental Theorems of the Laplace Transform
- Gambler's Ruin Problem
- Geometric Distribution
- Geometry
- Graph
- Graph Fusion
- Graph Theory
- Graphical Representations of Statistical Data
- Handshaking Lemma
- Hanging Vertex
- Hasse Diagram
- Havel-Hakimi Algorithm
- Height of Tree
- Hermite's Interpolation Method
- Histogram
- Identity Matrix
- Identity Transformation
- Image and Preimage of a Function
- Improper Integral
- Increasing and Decreasing Sequence
- Independent and Identically Distributed Random Variables
- Independent Trial Process
- Indicator Random Variable
- Inferential Statistics
- Infinite Collection of Sets
- Initial Probability Vector
- Injective Linear Transformation
- Inner Product
- Integral of a Surface
- Integral of a Vector Field over a Surface
- Integral Transform
- Interior Point
- Internal and External Degrees of a Vertex
- Interpolation
- Interquartile Range
- Intersection of Graphs
- Inverse Linear Transformation
- Inverse Relation
- Isomorphic Graphs
- Isomorphism
- Jacobian Matrix
- Kurtosis
- Lagrange Polynomial
- Laplace Transform
- Laplace Transform Conditions of Existence
- Laplace Transform of Simple Functions
- Laplacian of a Function
- Lattice
- Law of Cosines
- Law of the Unconscious Statistician
- Leaf Vertex
- Length Between Vertices
- Length of a Path
- Level Set
- Likelihood Function
- Limit of a Sequence
- Limit of a Vector-Valued Function
- Limit Point
- Line
- Line Integral
- Line Intersection
- Linear Function
- Linear Inequality
- Linear Operator Determinant
- Linear Transformation
- Linear Transformation Addition
- Linear Transformation Composition
- Linear Transformation Scalar Multiplication
- Loop
- M-ary Tree
- M-M-S Queue
- Marginal Density Function
- Markov Chain
- Markov Chain State Class
- Markov Decision Process
- Markov Decision Process Policy
- Markov Process
- Markov Property
- Mathematical Model
- Matrix of a Relation
- Maximum Likelihood Method for Obtaining Estimators
- MDP as a Linear Programming Problem
- Mean Deviation
- Mean Squared Error
- Measure of Association
- Measure of Central Tendency
- Measure of Dispersion
- Measure of Shape
- Median
- Median for a Set of Frequencies
- Metric Space
- Minimal and Maximal
- Minimum and Maximum
- Mode
- Moment
- Moment-Generating Function
- Moment-Generating Function of the Sum of the Random Variables in a Random Sample
- Moments Method for Obtaining Estimators
- Multi-Edge
- Multidigraph
- Multiplication Principle
- n Step Transition Probability
- Newton's Divided Differences Interpolation Method
- Newton's Finite Differences Interpolation Method
- Norm
- Norm under Real Numbers
- Normal Distribution
- Normal Unit Vector
- Normalised Form of Real Numbers
- Normative Mathematical Model
- Number of Combinations
- One Step Transition Probability
- Open Ball
- Open Cover
- Open Neighbourhood
- Open Set
- Operations of Limits of Sequences
- Optimisation Methods for Markov Decision Processes
- Order Relation
- Order Statistic
- Orthogonal Complement
- Orthogonal Matrix
- Orthogonal Projection of a Vector
- Orthogonal Transformation
- Orthonormal and Orthogonal Set
- Parallel Arcs
- Parallel Lines
- Parameter (Statistics)
- Parameter Set
- Parameter Space
- Partial Fraction Decomposition
- Partially Ordered Set
- Partition of a Sample Space
- Partition of a Set
- Path
- Path Concatenation
- Path Integral
- Path Integral Applications
- Pearson's Correlation Coefficient
- Permutation
- Permutations with Groups of Equal Elements
- Permutations with no Repetitions
- Permutations with Repetitions
- Pigeonhole Principle
- Plane
- Plane Intersection
- Planes and Points
- Point Process
- Poisson Distribution
- Policy Improvement Method for MDPs
- Population
- Potential Function
- Powers of a Relation
- Probabilities with a Distribution Function
- Probability Measure
- Probability of Absorption
- Probability of an Event
- Probability of Ruin in the Gambler's Ruin Problem
- Probability Space
- Product of an Associated Matrix and a Coordinate Vector
- Product Rule
- Proper Subgraph
- Properties of a Characteristic Function
- Properties of a Distribution Function
- Properties of a Moment-Generating Function
- Properties of a Probability Measure
- Properties of Relations
- Properties of Relations in their Representations
- Properties of the Expected Value
- Pseudodigraph
- Qualitative Variable
- Quantile
- Quantitative Variable
- Quotient Set
- Random Sample
- Random Variable
- Random Variable Realisation
- Random Vector
- Random Walk
- Range (Measure of Dispersion)
- Range of a Function
- Real Numbers as a Vector Space
- Recurrence Time
- Recurring Arcs
- Regular Digraph
- Regular Graph
- Regular Markov Chain
- Relating Associated Matrices and Changes of Basis
- Relation
- Relations as a Set
- Relative Error
- Ring Sum of Graphs
- Root Vertex
- Rooted Tree
- Rounding Error
- Sample
- Sample Space
- Sample Statistic
- Sampling Distribution
- Sampling Distribution of the Variance of a Normally Distributed Random Sample
- Sampling Distribution of the Variance of a Normally Distributed Random Sample with an Unknown Expected Value
- Scientific Method in Statistics
- Secant Method
- Sequence
- Sequence of Random Variables
- Series
- Shifted Geometric Distribution
- Shifted Unit Step Function
- Simple Digraph
- Simple Graph
- Simple Trajectory
- Skewness
- Smooth Curve
- Stability of a Numerical Method
- Standard Deviation
- Standard Normal Distribution
- State Communication
- State Set
- Stationary Process
- Stationary Transition Probability
- Statistics
- Steady State Probability
- Stochastic Process
- Stochastic Process with Independent Increments
- Strongly Connected Graph
- Student's T-Distribution
- Subgraph
- Subjacent Graph
- Subsequence
- Successive Approximations Method for MDPs
- Sum of Graphs
- Supremum and Infimum
- Surjective Linear Transformations
- Symmetric Digraph
- Tangent Unit Vector
- Tangential and Normal Components of Acceleration
- Taylor Polynomial
- Taylor Series
- Taylor Theorem
- Theorems of Limits in a Probability Measure
- Time Series
- Total Order Relation
- Total Probability Formula
- Transition Matrix
- Transition Probabilities in a Markov Chain
- Transition Probabilities in a Random Walk
- Transitory Set
- Tree
- Two Line Cases
- Types of Digraphs
- Types of Graphs
- Types of Paths
- Types of Stochastic Processes
- Types of Trees
- Types of Vertices in a Digraph
- Unbiased Estimator
- Unconditional Transition Probability
- Uniformly Minimum-Variance Unbiased Estimator
- Union of Graphs
- Unit Step Function
- Upper and Lower Bounds
- Variable (Statistics)
- Variance
- Vector Field
- Vector Space
- Vector-Valued Function
- Vectorial Function
- Vertex
- Vertex Degree
- Vertex-Disjoint Subgraphs
- Weighted Mean
- Well-Order
- σ-Algebra
- A Constant Desire to Fix Things Keeps Them Broken
- Action Leads to Motivation
- Boredom Leads to Creativity
- Engaging Less with Intrusive Thoughts Makes Them Less Common
- Focus on the Habit Cue, not the Behaviour
- Good Feedback is Constructive and Actionable
- Habit
- Habits are Built By Getting Used to the Habit First
- I Am Not Responsible for How Others Perceive Me
- Identifying When Thoughts Drift Away From Reality is Key to Stop Overthinking
- If This, Then That Patterns as a Way of Being More Mindful
- Other People Don't Know Me as Well as I Do
- Others' Perception of Me Doesn't Define Who I Am
- Overthinking is Seldom About Reality
- Productivity is Doing the Right Things in the Right Amounts of Time
- Self-Awareness
- Small Actions Compound Over Time
- Time is a Social Construct
- Time is Going To Pass Whether You Start Something or Not
- Too Much Music Can Be a Bad Thing
- We Always Have Personal Influence Over Our Life
- What We Do to Achieve Our Goals Should Be Fun
- A Zettelkasten Forces You to Do Your Own Thinking
- A Zettelkasten is a Journey, Not a Destination
- A Zettelkasten isn't Like Wikipedia
- A Zettelkasten Makes Concepts Easily Accessible
- Atomicity
- Brains are Better at Thinking than at Storing Information
- Exercising the Brain is Just Like Exercising a Muscle
- Learning is Just Like Exercising a Muscle
- Notes in a Zettelkasten Have No Finished State
- Perfectionism Has No Place in a Zettelkasten
- The Value of a Zettelkasten in University
- Writing in a Zettelkasten Should Be Frictionless
- Zettelkasten